Abstract The Gerber-Shiu function provides a unified framework for the evaluation of a
variety of risk quantities. Ever since its establishment, it has attracted constantly increasing …

The main purpose of the book is to show how a viscosity approach can be used to tackle
control problems in insurance. The problems covered are the maximization of survival …

This paper investigates the first passage times to flat boundaries for hyper-exponential jump
(diffusion) processes. Explicit solutions of the Laplace transforms of the distribution of the …

This paper concerns an optimal dividend distribution problem for an insurance company
whose risk process evolves as a spectrally negative Lévy process (in the absence of …

This paper provides a new and accessible approach to establishing certain results
concerning the discounted penalty function. The direct approach consists of two steps. In the …

In this article we present a sequence of random variables with weighted tail distribution
functions, constructed based on the relevation transform. For this sequence, we prove …

This paper considers a renewal insurance risk model with two-sided jumps (eg Labbé et al.,
2011), where downward and upward jumps typically represent claim amounts and random …

An insurance risk model where claims follow a Markovian arrival process (MArP) is
considered in this paper. It is shown that the expected present value of total operating costs …

Given two absolutely continuous nonnegative independent random variables, we define the
reversed relevation transform as dual to the relevation transform. We first apply such …

This paper studies the Parisian ruin problem first proposed by Dassios and Wu (2008a, b),
where the Parisian ruin time is defined to be the first time when the surplus process has …